1. Marcin Gruszecki S. Vasheghani Farahani, V. Nakariakov, T. Arber Magnetacoustic shock formation near a magnetic null point

2. Outline of my talk 1.Introduction, 2.Specific questions, 3.Numerical setup, 4. Numerical results, 5. Conclusions.

3. Interaction MHD waves with magnetic null points is interesting in the context of flare triggering and generation of quasi-periodic pulsations (e.g. through the generation of current density spikes and hence anomalous resistivity) 1)Craig & Watson (1992) considered waves in the neighbourhood of X-point. They showed that waves generate an exponentially large increase in the current density. 2)Ofman et al (1993) studied reconnection and relaxation of 2D X-point using resistive MHD equations. They showed that the interaction between the plasma flow velocity and the magnetic field is the important physical effect. 3)McLauglin & Hood in series of papers investigated behaviour of fast MHD waves near X-point. They concluded that waves are refracted around and accumulated at the null point. Introduction

4. 1.Study the effect of nonlinear steepening of a fast magnetoacoustic wave near a null point. 2.Find a distance of magnetoacoustic shock formation from the magnetic null point as a function of initial wave length, amplitude. 3.What kind of pulses can reach the magnetic null point and ignite the magnetic reconnection, i.e. seed the anomalous resistivity close enough to null point. Can it explain the phenomenon of sympathetic flares. 4.Compare numerical results with the linear analytical solution. Specific questions

5. Analitical model Numerical result s were obtained with use LARE2D code (Arber T. et al. 2001)

6. Initial setup B = B 0 [x/L, -y/L, 0] ρ [kg/m 3 ]B [T]T [K]c s [Mm/s]V A [Mm/s]β 10 -12 10 -3 6·10 5 0.1290.90.025

7. Initial pulse c.f. McLaughlin et al. 2008

8. Comparison of numerical results with linear analitical solution Analitical solution A 0 =1 A 0 =0.01 A 0 = 0.1 A 0 = 0.5 Larger amplitude waves travel faster

9. Creation of shock 0.7s 1.0s 1.4s 0.4s 0.6s 0.8s

10. Paremetric studies 0.9·exp(-0.9·x) 0.35·ln(x)+0.91

11. Conclusions 1.We showed the creation of shock fast magnetoacoustic wave in vicinity of magnetic X - point. The shock is accompanied with a spike of current density, hence anomalous resistivity can be generated. 2.Small amplitudes pulse are coincide with the linear analytical solution Craig and McClymont (1991). 3.Larger amplitude waves propagate faster. 4.We performed parametric studies by varying both width and strength of the initial pulse. Only wider and small amplitude pulses can reach magnetic X - point before overturning and ignite magnetic reconnection. 5. Narrower and high amplitude pulses overturn faster.

12. Thank you